Optimal control and inverse problems in radiative heat transfer

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The main objective of this project is the derivation and investigation of efficient mathematical methods for the solution of optimal control and identification problems for radiation dominant processes, which are described by a nonlinear integro-differential system or diffusive type approximations. These processes are for example relevant in glass production or in the layout of gas turbine combustion chambers. Since already their simulation is very complex and time consuming due to the radiation, the main focus of the project will be on the investigation of optimization algorithms based on the adjoint variables, which will be applied to the full radiative heat transfer system as well as to diffusive type approximations. In contrast to black-box optimization algorithms, this allows to keep a balance between the optimization and simulation effort for arbitrary fine discretizations. Special focus will be on the investigation of different numerical methods which allow to solve three dimensional problems at reasonable computational costs. In addition to the optimization we will also study new approaches to the reconstruction of the initial temperature from boundary measurements, since its precise knowledge is mandatory for any satisfactory simulation. Especially, we will develop a fast, derivative-free method for the solution of the inverse problem, such that we can use many different models for the simulation of the radiative process.